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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 352800.gp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.gp1 | 352800gp1 | \([0, 0, 0, -237405, -44521400]\) | \(2156689088/81\) | \(55576446408000\) | \([2]\) | \(1769472\) | \(1.7238\) | \(\Gamma_0(N)\)-optimal |
| 352800.gp2 | 352800gp2 | \([0, 0, 0, -226380, -48843200]\) | \(-29218112/6561\) | \(-288108298179072000\) | \([2]\) | \(3538944\) | \(2.0704\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.gp have rank \(1\).
Complex multiplication
The elliptic curves in class 352800.gp do not have complex multiplication.Modular form 352800.2.a.gp
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
